Environmental Engineering Reference
In-Depth Information
focus. The concept of elasticity is widely used in conservation biology; examples
are given by Benton and Grant (1999), Pascarella and Horvitz (1998), Heppel et al.
(2000) and Pichancourt et al. (2006).
For the red deer example given in Table
9.1
the following elasticity matrix is
evaluated:
0
1
0
0
0
:
038 0
:
029 0
:
027 0
:
029 0
:
028 0
:
016 0
:
009 0
:
005
@
A
0
:
181
0
:
181
0
:
143
0
:
113
E
¼
0
:
087
0
:
058
:
0
030
:
0
014
:
:
0
005 0
007
Based on these elasticity values, it is apparent that the survival rates of the first
two or three age classes are much more important for the growth of the red deer
population than any of the fertility rates. Any measure to control the population
should therefore focus on these parameters.
9.3 The Extended Leslie Model
In the original Leslie model there are several restrictions that should be mentioned:
First, up to now we have dealt with a constant environment. To consider fluctuating
environmental conditions (e.g. temperature) that play a crucial role in insect
development, other concepts are needed. One possible way to do this is to translate
the real time into another unit, taking into account the environmental conditions.
This alternative unit is called the biological time (or biological age, as well) and it
measures (to a certain extent) the state of development of individuals (Sondgerath
and Muller-Pietralla 1996; Schroder and Sondgerath 1996).
The concept of biological time is as follows: consider a population whose
development will last 100 days under constant optimal conditions. The develop-
ment rate for this population is defined as 1/100
¼
0.01/day. Summing up the
development rates after 100 days will yield a value of 1 (the time the development
is complete).
Real conditions are never constant, so a formulation of the development rate
dependent on environmental conditions is needed. For the most important environ-
mental factor (the temperature), this relationship is often an optimum curve which,
for example, can be described by an O'Neill function (Spain 1982) depending on
parameters
r
max
(maximal development rate under optimal temperature),
T
opt
,
T
max
(optimal and maximal temperature, respectively) and the Q10-value, which describes
